In 1934, the philosopher Paul Weiss called Peirce "the most original and versatile of American philosophers and America's greatest logician".[10]Webster's Biographical Dictionary said in 1943 that Peirce was "now regarded as the most original thinker and greatest logician of his time."[11]

Peirce suffered from his late teens onward from a nervous condition then known as "facial neuralgia", which would today be diagnosed as trigeminal neuralgia. Brent says that when in the throes of its pain "he was, at first, almost stupefied, and then aloof, cold, depressed, extremely suspicious, impatient of the slightest crossing, and subject to violent outbursts of temper".[18] Its consequences may have led to the social isolation which made his life's later years so tragic.

During the 1880s, Peirce's indifference to bureaucratic detail waxed while his Survey work's quality and timeliness waned. Peirce took years to write reports that he should have completed in months.[according to whom?] Meanwhile, he wrote entries, ultimately thousands during 1883–1909, on philosophy, logic, science, and other subjects for the encyclopedic Century Dictionary.[28] In 1885, an investigation by the Allison Commission exonerated Peirce, but led to the dismissal of Superintendent Julius Hilgard and several other Coast Survey employees for misuse of public funds.[29] In 1891, Peirce resigned from the Coast Survey at Superintendent Thomas Corwin Mendenhall's request.[30] He never again held regular employment.

Brent documents something Peirce never suspected, namely that his efforts to obtain academic employment, grants, and scientific respectability were repeatedly frustrated by the covert opposition of a major Canadian-American scientist of the day, Simon Newcomb.[32] Peirce's efforts may also have been hampered by a difficult personality; Brent conjectures as to further psychological difficulty.[33]

Peirce's personal life worked against his professional success. After his first wife, Harriet Melusina Fay ("Zina"), left him in 1875,[34] Peirce, while still legally married, became involved with Juliette, whose name, given variously as Froissy and Pourtalai[35] and nationality (she spoke French[36]) remain uncertain.[37] When his divorce from Zina became final in 1883, he married Juliette.[38] That year, Newcomb pointed out to a Johns Hopkins trustee that Peirce, while a Hopkins employee, had lived and traveled with a woman to whom he was not married; the ensuing scandal led to his dismissal in January 1884.[39] Over the years Peirce sought academic employment at various universities without success.[40] He had no children by either marriage.[41]

Cambridge, where Peirce was born and raised, New York City, where he often visited and sometimes lived, and Milford, where he spent the later years of his life with his second wife Juliette.

In 1887 Peirce spent part of his inheritance from his parents to buy 2,000 acres (8 km2) of rural land near Milford, Pennsylvania, which never yielded an economic return.[42] There he had an 1854 farmhouse remodeled to his design.[43] The Peirces named the property "Arisbe". There they lived with few interruptions for the rest of their lives,[44] Charles writing prolifically, much of it unpublished to this day (see Works). Living beyond their means soon led to grave financial and legal difficulties.[45] He spent much of his last two decades unable to afford heat in winter and subsisting on old bread donated by the local baker. Unable to afford new stationery, he wrote on the verso side of old manuscripts. An outstanding warrant for assault and unpaid debts led to his being a fugitive in New York City for a while.[46] Several people, including his brother James Mills Peirce[47] and his neighbors, relatives of Gifford Pinchot, settled his debts and paid his property taxes and mortgage.[48]

Peirce did some scientific and engineering consulting and wrote much for meager pay, mainly encyclopedic dictionary entries, and reviews for The Nation (with whose editor, Wendell Phillips Garrison, he became friendly). He did translations for the Smithsonian Institution, at its director Samuel Langley's instigation. Peirce also did substantial mathematical calculations for Langley's research on powered flight. Hoping to make money, Peirce tried inventing.[49] He began but did not complete a number of books.[50] In 1888, President Grover Cleveland appointed him to the Assay Commission.[51]

The one who did the most to help Peirce in these desperate times was his old friend William James, dedicating his Will to Believe (1897) to Peirce, and arranging for Peirce to be paid to give two series of lectures at or near Harvard (1898 and 1903).[56] Most important, each year from 1907 until James's death in 1910, James wrote to his friends in the Boston intelligentsia to request financial aid for Peirce; the fund continued even after James died. Peirce reciprocated by designating James's eldest son as his heir should Juliette predecease him.[57] It has been believed that this was also why Peirce used "Santiago" ("St. James" in English) as a middle name, but he appeared in print as early as 1890 as Charles Santiago Peirce. (See Charles Santiago Sanders Peirce for discussion and references).

Peirce grew up in a home where the supremacy of the white Anglo-Saxon male was taken for granted, Irish immigrants were considered inferior and Negro slavery was considered natural.[58]

Until the outbreak of the Civil War his father described himself as a secessionist, but after the outbreak of the war, this stopped and he became a Union partisan, supporting the Sanitary Commission, the leading Northern war charity with money. No members of the Peirce family volunteered or enlisted. Peirce shared his father's views and liked to use the syllogism

All Men are equal in their political rights
Negroes are Men
- Negroes are equal in political rights to white

Bertrand Russell (1959) wrote,[60] "Beyond doubt [...] he was one of the most original minds of the later nineteenth century, and certainly the greatest American thinker ever." (Russell and Whitehead's Principia Mathematica, published from 1910 to 1913, does not mention Peirce; Peirce's work was not widely known till later.)[61]A. N. Whitehead, while reading some of Peirce's unpublished manuscripts soon after arriving at Harvard in 1924, was struck by how Peirce had anticipated his own "process" thinking. (On Peirce and process metaphysics, see Lowe 1964.[25]) Karl Popper viewed Peirce as "one of the greatest philosophers of all times".[62] Yet Peirce's achievements were not immediately recognized. His imposing contemporaries William James and Josiah Royce[63] admired him, and Cassius Jackson Keyser at Columbia and C. K. Ogden wrote about Peirce with respect, but to no immediate effect.

The first scholar to give Peirce his considered professional attention was Royce's student Morris Raphael Cohen, the editor of an anthology of Peirce's writings titled Chance, Love, and Logic (1923) and the author of the first bibliography of Peirce's scattered writings.[64]John Dewey studied under Peirce at Johns Hopkins[31] and, from 1916 onwards, Dewey's writings repeatedly mention Peirce with deference. His 1938 Logic: The Theory of Inquiry is much influenced by Peirce.[65] The publication of the first six volumes of the Collected Papers (1931–35), the most important event to date in Peirce studies and one that Cohen made possible by raising the needed funds,[66] did not prompt an outpouring of secondary studies. The editors of those volumes, Charles Hartshorne and Paul Weiss, did not become Peirce specialists. Early landmarks of the secondary literature include the monographs by Buchler (1939), Feibleman (1946), and Goudge (1950), the 1941 Ph.D. thesis by Arthur W. Burks (who went on to edit volumes 7 and 8), and the studies edited by Wiener and Young (1952). The Charles S. Peirce Society was founded in 1946. Its Transactions, an academic quarterly specializing in Peirce, pragmatism, and American philosophy, has appeared since 1965.

In 1949, while doing unrelated archival work, the historian of mathematics Carolyn Eisele (1902–2000) chanced on an autograph letter by Peirce. So began her 40 years of research on Peirce the mathematician and scientist, culminating in Eisele (1976, 1979, 1985). Beginning around 1960, the philosopher and historian of ideasMax Fisch (1900–1995) emerged as an authority on Peirce; Fisch (1986)[67] includes many of his relevant articles, including a wide-ranging survey (Fisch 1986: 422–48) of the impact of Peirce's thought through 1983.

Currently, considerable interest is being taken in Peirce's ideas by researchers wholly outside the arena of academic philosophy. The interest comes from industry, business, technology, intelligence organizations, and the military; and it has resulted in the existence of a substantial number of agencies, institutes, businesses, and laboratories in which ongoing research into and development of Peircean concepts are being vigorously undertaken.

Harvard University obtained from Peirce's widow soon after his death the papers found in his study, but did not microfilm them until 1964. Only after Richard Robin (1967)[70] catalogued this Nachlass did it become clear that Peirce had left approximately 1650 unpublished manuscripts, totaling over 100,000 pages,[71] mostly still unpublished except on microfilm. On the vicissitudes of Peirce's papers, see Houser (1989).[72] Reportedly the papers remain in unsatisfactory condition.[73]

1931–58: Collected Papers of Charles Sanders Peirce (CP), 8 volumes, includes many published works, along with a selection of previously unpublished work and a smattering of his correspondence. This long-time standard edition drawn from Peirce's work from the 1860s to 1913 remains the most comprehensive survey of his prolific output from 1893 to 1913. It is organized thematically, but texts (including lecture series) are often split up across volumes, while texts from various stages in Peirce's development are often combined, requiring frequent visits to editors' notes.[75] Edited (1–6) by Charles Hartshorne and Paul Weiss and (7–8) by Arthur Burks, in print and online.

1976: The New Elements of Mathematics by Charles S. Peirce, 4 volumes in 5, included many previously unpublished Peirce manuscripts on mathematical subjects, along with Peirce's important published mathematical articles. Edited by Carolyn Eisele, back in print.

1982–now: Writings of Charles S. Peirce, A Chronological Edition (W), Volumes 1–6 & 8, of a projected 30. The limited coverage, and defective editing and organization, of the Collected Papers led Max Fisch and others in the 1970s to found the Peirce Edition Project (PEP), whose mission is to prepare a more complete critical chronological edition. Only seven volumes have appeared to date, but they cover the period from 1859–1892, when Peirce carried out much of his best-known work. W 8 was published in November 2010; and work continues on W 7, 9, and 11. In print and online.

1985: Historical Perspectives on Peirce's Logic of Science: A History of Science, 2 volumes. Auspitz has said,[76] "The extent of Peirce's immersion in the science of his day is evident in his reviews in the Nation [...] and in his papers, grant applications, and publishers' prospectuses in the history and practice of science", referring latterly to Historical Perspectives. Edited by Carolyn Eisele, back in print.

1992–98: The Essential Peirce (EP), 2 volumes, is an important recent sampler of Peirce's philosophical writings. Edited (1) by Nathan Hauser and Christian Kloesel and (2) by PEP editors, in print.

1997: Pragmatism as a Principle and Method of Right Thinking collects Peirce's 1903 Harvard "Lectures on Pragmatism" in a study edition, including drafts, of Peirce's lecture manuscripts, which had been previously published in abridged form; the lectures now also appear in EP 2. Edited by Patricia Ann Turisi, in print.

In 1885[81] he distinguished between first-order and second-order quantification.[82][83] In the same paper he set out what can be read as the first (primitive) axiomatic set theory, anticipating Zermelo by about two decades (Brady 2000,[84] pp. 132–3).

In 1886 he saw that Boolean calculations could be carried out via electrical switches,[12] anticipating Claude Shannon by more than 50 years.

Peirce wrote drafts for an introductory textbook, with the working title The New Elements of Mathematics, that presented mathematics from an original standpoint. Those drafts and many other of his previously unpublished mathematical manuscripts finally appeared[77] in The New Elements of Mathematics by Charles S. Peirce (1976), edited by mathematician Carolyn Eisele.

Nature of mathematics

Peirce agreed with Auguste Comte in regarding mathematics as more basic than philosophy and the special sciences (of nature and mind). Peirce classified mathematics into three subareas: (1) mathematics of logic, (2) discrete series, and (3) pseudo-continua (as he called them, including the real numbers) and continua. Influenced by his father Benjamin, Peirce argued that mathematics studies purely hypothetical objects and is not just the science of quantity but is more broadly the science which draws necessary conclusions; that mathematics aids logic, not vice versa; and that logic itself is part of philosophy and is the science about drawing conclusions necessary and otherwise.[86]

On the Algebra of Logic: A Contribution to the
Philosophy of Notation (1884/1885)

The Logic of Relatives (1897)

The Simplest Mathematics (1902 MS)

Prolegomena To an Apology For Pragmaticism (1906,
on existential graphs)

Beginning with his first paper on the "Logic of Relatives" (1870), Peirce extended the theory of relations that Augustus De Morgan had just recently awakened from its Cinderella slumbers. Much of the mathematics of relations now taken for granted was "borrowed" from Peirce, not always with all due credit; on that and on how the young Bertrand Russell, especially his Principles of Mathematics and Principia Mathematica, did not do Peirce justice, see Anellis (1995).[61] In 1918 the logician C. I. Lewis wrote, "The contributions of C.S. Peirce to symbolic logic are more numerous and varied than those of any other writer — at least in the nineteenth century."[87] Beginning in 1940, Alfred Tarski and his students rediscovered aspects of Peirce's larger vision of relational logic, developing the perspective of relation algebra.

On Peirce and his contemporaries Ernst Schröder and Gottlob Frege, Hilary Putnam (1982)[82] documented that Frege's work on the logic of quantifiers had little influence on his contemporaries, although it was published four years before the work of Peirce and his student Oscar Howard Mitchell. Putnam found that mathematicians and logicians learned about the logic of quantifiers through the independent work of Peirce and Mitchell, particularly through Peirce's "On the Algebra of Logic: A Contribution to the Philosophy of Notation"[81] (1885), published in the premier American mathematical journal of the day, and cited by Peano and Schröder, among others, who ignored Frege. They also adopted and modified Peirce's notations, typographical variants of those now used. Peirce apparently was ignorant of Frege's work, despite their overlapping achievements in logic, philosophy of language, and the foundations of mathematics.

The Polish school of logic and foundational mathematics, including Alfred Tarski;

Arthur Prior, who praised and studied Peirce's logical work in a 1964 paper[25] and in Formal Logic (saying on page 4 that Peirce "perhaps had a keener eye for essentials than any other logician before or since.").

A philosophy of logic, grounded in his categories and semiotic, can be extracted from Peirce's writings and, along with Peirce's logical work more generally, is exposited and defended in Hilary Putnam (1982);[82] the Introduction in Nathan Houser et al. (1997);[90] and Randall Dipert's chapter in Cheryl Misak (2004).[91]

Continuity and synechism are central in Peirce's philosophy: "I did not at first suppose that it was, as I gradually came to find it, the master-Key of philosophy".[92]

From a mathematical point of view, he embraced infinitesimals and worked long on the mathematics of continua. He long held that the real numbers constitute a pseudo-continuum;[93] that a true continuum is the real subject matter of analysis situs (topology); and that a true continuum of instants exceeds—and within any lapse of time has room for—any Aleph number (any infinite multitude as he called it) of instants.[94]

In 1908 Peirce wrote that he found that a true continuum might have or lack such room. Jérôme Havenel (2008): "It is on May 26, 1908, that Peirce finally gave up his idea that in every continuum there is room for whatever collection of any multitude. From now on, there are different kinds of continua, which have different properties."[95]

It is not sufficiently recognized that Peirce's career was that of a scientist, not a philosopher; and that during his lifetime he was known and valued chiefly as a scientist, only secondarily as a logician, and scarcely at all as a philosopher. Even his work in philosophy and logic will not be understood until this fact becomes a standing premise of Peircean studies.

Peirce's philosophy includes (see below in related sections) a pervasive three-category system, belief that truth is immutable and is both independent from actual opinion (fallibilism) and discoverable (no radical skepticism), logic as formal semiotic on signs, on arguments, and on inquiry's ways—including philosophical pragmatism (which he founded), critical common-sensism, and scientific method—and, in metaphysics: Scholastic realism, e.g. John Duns Scotus, belief in God, freedom, and at least an attenuated immortality, objective idealism, and belief in the reality of continuity and of absolute chance, mechanical necessity, and creative love. In his work, fallibilism and pragmatism may seem to work somewhat like skepticism and positivism, respectively, in others' work. However, for Peirce, fallibilism is balanced by an anti-skepticism and is a basis for belief in the reality of absolute chance and of continuity,[99] and pragmatism commits one to anti-nominalist belief in the reality of the general (CP 5.453–7).

For Peirce, First Philosophy, which he also called cenoscopy, is less basic than mathematics and more basic than the special sciences (of nature and mind). It studies positive phenomena in general, phenomena available to any person at any waking moment, and does not settle questions by resorting to special experiences.[100] He divided such philosophy into (1) phenomenology (which he also called phaneroscopy or categorics), (2) normative sciences (esthetics, ethics, and logic), and (3) metaphysics; his views on them are discussed in order below.

On May 14, 1867, the 27-year-old Peirce presented a paper entitled "On a New List of Categories" to the American Academy of Arts and Sciences, which published it the following year. The paper outlined a theory of predication, involving three universal categories that Peirce developed in response to reading Aristotle, Kant, and Hegel, categories that Peirce applied throughout his work for the rest of his life.[19] Peirce scholars generally regard the "New List" as foundational or breaking the ground for Peirce's "architectonic", his blueprint for a pragmatic philosophy. In the categories one will discern, concentrated, the pattern that one finds formed by the three grades of clearness in "How To Make Our Ideas Clear" (1878 paper foundational to pragmatism), and in numerous other trichotomies in his work.

"On a New List of Categories" is cast as a Kantian deduction; it is short but dense and difficult to summarize. The following table is compiled from that and later works.[101] In 1893, Peirce restated most of it for a less advanced audience.[102]

Peirce did not write extensively in aesthetics and ethics,[109] but came by 1902 to hold that aesthetics, ethics, and logic, in that order, comprise the normative sciences.[110] He characterized aesthetics as the study of the good (grasped as the admirable), and thus of the ends governing all conduct and thought.[111]

Peirce regarded logic per se as a division of philosophy, as a normative science based on esthetics and ethics, as more basic than metaphysics,[112] and as "the art of devising methods of research".[113] More generally, as inference, "logic is rooted in the social principle", since inference depends on a standpoint that, in a sense, is unlimited.[114] Peirce called (with no sense of deprecation) "mathematics of logic" much of the kind of thing which, in current research and applications, is called simply "logic". He was productive in both (philosophical) logic and logic's mathematics, which were connected deeply in his work and thought.

Peirce argued that logic is formal semiotic, the formal study of signs in the broadest sense, not only signs that are artificial, linguistic, or symbolic, but also signs that are semblances or are indexical such as reactions. Peirce held that "all this universe is perfused with signs, if it is not composed exclusively of signs",[115] along with their representational and inferential relations. He argued that, since all thought takes time, all thought is in signs[116] and sign processes ("semiosis") such as the inquiry process. He divided logic into: (1) speculative grammar, or stechiology, on how signs can be meaningful and, in relation to that, what kinds of signs there are, how they combine, and how some embody or incorporate others; (2) logical critic, or logic proper, on the modes of inference; and (3) speculative or universal rhetoric, or methodeutic,[117] the philosophical theory of inquiry, including pragmatism.

In his "F.R.L." [First Rule of Logic] (1899), Peirce states that the first, and "in one sense, the sole", rule of reason is that, to learn, one needs to desire to learn and desire it without resting satisfied with that which one is inclined to think.[112] So, the first rule is, to wonder. Peirce proceeds to a critical theme in research practices and the shaping of theories:

...there follows one corollary which itself deserves to be inscribed upon every wall of the city of philosophy:

Do not block the way of inquiry.

Peirce adds, that method and economy are best in research but no outright sin inheres in trying any theory in the sense that the investigation via its trial adoption can proceed unimpeded and undiscouraged, and that "the one unpardonable offence" is a philosophical barricade against truth's advance, an offense to which "metaphysicians in all ages have shown themselves the most addicted". Peirce in many writings holds that logic precedes metaphysics (ontological, religious, and physical).

Peirce goes on to list four common barriers to inquiry: (1) Assertion of absolute certainty; (2) maintaining that something is absolutely unknowable; (3) maintaining that something is absolutely inexplicable because absolutely basic or ultimate; (4) holding that perfect exactitude is possible, especially such as to quite preclude unusual and anomalous phenomena. To refuse absolute theoretical certainty is the heart of fallibilism, which Peirce unfolds into refusals to set up any of the listed barriers. Peirce elsewhere argues (1897) that logic's presupposition of fallibilism leads at length to the view that chance and continuity are very real (tychism and synechism).[99]

The First Rule of Logic pertains to the mind's presuppositions in undertaking reason and logic, presuppositions, for instance, that truth and the real do not depend on yours or my opinion of them but do depend on representational relation and consist in the destined end in investigation taken far enough (see below). He describes such ideas as, collectively, hopes which, in particular cases, one is unable seriously to doubt.[118]

Peirce sought, through his wide-ranging studies through the decades, formal philosophical ways to articulate thought's processes, and also to explain the workings of science. These inextricably entangled questions of a dynamics of inquiry rooted in nature and nurture led him to develop his semiotic with very broadened conceptions of signs and inference, and, as its culmination, a theory of inquiry for the task of saying 'how science works' and devising research methods. This would be logic by the medieval definition taught for centuries: art of arts, science of sciences, having the way to the principles of all methods.[113] Influences radiate from points on parallel lines of inquiry in Aristotle's work, in such loci as: the basic terminology of psychology in On the Soul; the founding description of sign relations in On Interpretation; and the differentiation of inference into three modes that are commonly translated into English as abduction, deduction, and induction, in the Prior Analytics, as well as inference by analogy (called paradeigma by Aristotle), which Peirce regarded as involving the other three modes.

Peirce began writing on semiotic in the 1860s, around the time when he devised his system of three categories. He called it both semiotic and semeiotic. Both are current in singular and plural. He based it on the conception of a triadic sign relation, and defined semiosis as "action, or influence, which is, or involves, a cooperation of three subjects, such as a sign, its object, and its interpretant, this tri-relative influence not being in any way resolvable into actions between pairs".[122] As to signs in thought, Peirce emphasized the reverse:

To say, therefore, that thought cannot happen in an instant, but requires a time, is but another way of saying that every thought must be interpreted in another, or that all thought is in signs.

Peirce held that all thought is in signs, issuing in and from interpretation, where 'sign' is the word for the broadest variety of conceivable semblances, diagrams, metaphors, symptoms, signals, designations, symbols, texts, even mental concepts and ideas, all as determinations of a mind or quasi-mind, that which at least functions like a mind, as in the work of crystals or bees[123] — the focus is on sign action in general rather than on psychology, linguistics, or social studies (fields which he also pursued).

Inquiry is a kind of inference process, a manner of thinking and semiosis. Global divisions of ways for phenomena to stand as signs, and the subsumption of inquiry and thinking within inference as a sign process, enable the study of inquiry on semiotics' three levels:

Conditions for meaningfulness. Study of significatory elements and combinations, their grammar.

Validity, conditions for true representation. Critique of arguments in their various separate modes.

Conditions for determining interpretations. Methodology of inquiry in its mutually interacting modes.

Peirce uses examples often from common experience, but defines and discusses such things as assertion and interpretation in terms of philosophical logic. In a formal vein, Peirce said:

On the Definition of Logic. Logic is formal semiotic. A sign is something, A, which brings something, B, its interpretant sign, determined or created by it, into the same sort of correspondence (or a lower implied sort) with something, C, its object, as that in which itself stands to C. This definition no more involves any reference to human thought than does the definition of a line as the place within which a particle lies during a lapse of time. It is from this definition that I deduce the principles of logic by mathematical reasoning, and by mathematical reasoning that, I aver, will support criticism of Weierstrassian severity, and that is perfectly evident. The word "formal" in the definition is also defined.
—Peirce, "Carnegie Application", The New Elements of Mathematics v. 4, p. 54.

Anything is a sign — not absolutely as itself, but instead in some relation or other. The sign relation is the key. It defines three roles encompassing (1) the sign, (2) the sign's subject matter, called its object, and (3) the sign's meaning or ramification as formed into a kind of effect called its interpretant (a further sign, for example a translation). It is an irreducible triadic relation, according to Peirce. The roles are distinct even when the things that fill those roles are not. The roles are but three; a sign of an object leads to one or more interpretants, and, as signs, they lead to further interpretants.

Extension × intension = information. Two traditional approaches to sign relation, necessary though insufficient, are the way of extension (a sign's objects, also called breadth, denotation, or application) and the way of intension (the objects' characteristics, qualities, attributes referenced by the sign, also called depth, comprehension, significance, or connotation). Peirce adds a third, the way of information, including change of information, to integrate the other two approaches into a unified whole.[124] For example, because of the equation above, if a term's total amount of information stays the same, then the more that the term 'intends' or signifies about objects, the fewer are the objects to which the term 'extends' or applies.

Determination. A sign depends on its object in such a way as to represent its object — the object enables and, in a sense, determines the sign. A physically causal sense of this stands out when a sign consists in an indicative reaction. The interpretant depends likewise on both the sign and the object — an object determines a sign to determine an interpretant. But this determination is not a succession of dyadic events, like a row of toppling dominoes; sign determination is triadic. For example, an interpretant does not merely represent something which represented an object; instead an interpretant represents something as a sign representing the object. The object (be it a quality or fact or law or even fictional) determines the sign to an interpretant through one's collateral experience[125] with the object, in which the object is found or from which it is recalled, as when a sign consists in a chance semblance of an absent object. Peirce used the word "determine" not in a strictly deterministic sense, but in a sense of "specializes," bestimmt,[126] involving variable amount, like an influence.[127] Peirce came to define representation and interpretation in terms of (triadic) determination.[128] The object determines the sign to determine another sign — the interpretant — to be related to the object as the sign is related to the object, hence the interpretant, fulfilling its function as sign of the object, determines a further interpretant sign. The process is logically structured to perpetuate itself, and is definitive of sign, object, and interpretant in general.[127]

Peirce held there are exactly three basic elements in semiosis (sign action):

A sign (or representamen)[129] represents, in the broadest possible sense of "represents". It is something interpretable as saying something about something. It is not necessarily symbolic, linguistic, or artificial—a cloud might be a sign of rain for instance, or ruins the sign of ancient civilization.[130] As Peirce sometimes put it (he defined sign at least 76 times[127]), the sign stands for the object to the interpretant. A sign represents its object in some respect, which respect is the sign's ground.[105]

An object (or semiotic object) is a subject matter of a sign and an interpretant. It can be anything thinkable, a quality, an occurrence, a rule, etc., even fictional, such as Prince Hamlet.[131] All of those are special or partial objects. The object most accurately is the universe of discourse to which the partial or special object belongs.[131] For instance, a perturbation of Pluto's orbit is a sign about Pluto but ultimately not only about Pluto. An object either (i) is immediate to a sign and is the object as represented in the sign or (ii) is a dynamic object, the object as it really is, on which the immediate object is founded "as on bedrock".[132]

An interpretant (or interpretant sign) is a sign's meaning or ramification as formed into a kind of idea or effect, an interpretation, human or otherwise. An interpretant is a sign (a) of the object and (b) of the interpretant's "predecessor" (the interpreted sign) as a sign of the same object. An interpretant either (i) is immediate to a sign and is a kind of quality or possibility such as a word's usual meaning, or (ii) is a dynamic interpretant, such as a state of agitation, or (iii) is a final or normal interpretant, a sum of the lessons which a sufficiently considered sign would have as effects on practice, and with which an actual interpretant may at most coincide.

Some of the understanding needed by the mind depends on familiarity with the object. To know what a given sign denotes, the mind needs some experience of that sign's object, experience outside of, and collateral to, that sign or sign system. In that context Peirce speaks of collateral experience, collateral observation, collateral acquaintance, all in much the same terms.[125]

Among Peirce's many sign typologies, three stand out, interlocked. The first typology depends on the sign itself, the second on how the sign stands for its denoted object, and the third on how the sign stands for its object to its interpretant. Also, each of the three typologies is a three-way division, a trichotomy, via Peirce's three phenomenological categories: (1) quality of feeling, (2) reaction, resistance, and (3) representation, mediation.[133]

I. Qualisign, sinsign, legisign (also called tone, token, type, and also called potisign, actisign, famisign):[134] This typology classifies every sign according to the sign's own phenomenological category—the qualisign is a quality, a possibility, a "First"; the sinsign is a reaction or resistance, a singular object, an actual event or fact, a "Second"; and the legisign is a habit, a rule, a representational relation, a "Third".

II. Icon, index, symbol: This typology, the best known one, classifies every sign according to the category of the sign's way of denoting its object—the icon (also called semblance or likeness) by a quality of its own, the index by factual connection to its object, and the symbol by a habit or rule for its interpretant.

III. Rheme, dicisign, argument (also called sumisign, dicisign, suadisign, also seme, pheme, delome,[134] and regarded as very broadened versions of the traditional term, proposition, argument): This typology classifies every sign according to the category which the interpretant attributes to the sign's way of denoting its object—the rheme, for example a term, is a sign interpreted to represent its object in respect of quality; the dicisign, for example a proposition, is a sign interpreted to represent its object in respect of fact; and the argument is a sign interpreted to represent its object in respect of habit or law. This is the culminating typology of the three, where the sign is understood as a structural element of inference.

Every sign belongs to one class or another within (I) and within (II) and within (III). Thus each of the three typologies is a three-valued parameter for every sign. The three parameters are not independent of each other; many co-classifications are absent, for reasons pertaining to the lack of either habit-taking or singular reaction in a quality, and the lack of habit-taking in a singular reaction. The result is not 27 but instead ten classes of signs fully specified at this level of analysis.

Borrowing a brace of concepts from Aristotle, Peirce examined three basic modes of inference — abduction, deduction, and induction — in his "critique of arguments" or "logic proper". Peirce also called abduction "retroduction", "presumption", and, earliest of all, "hypothesis". He characterized it as guessing and as inference to an explanatory hypothesis. He sometimes expounded the modes of inference by transformations of the categorical syllogism Barbara (AAA), for example in "Deduction, Induction, and Hypothesis" (1878).[135] He does this by rearranging the rule (Barbara's major premise), the case (Barbara's minor premise), and the result (Barbara's conclusion):

Deduction.

Rule: All the beans from this bag are white.Case: These beans are from this bag.Result: These beans are white.

Induction.

Case: These beans are [randomly selected] from this bag.Result: These beans are white.Rule: All the beans from this bag are white.

Hypothesis (Abduction).

Rule: All the beans from this bag are white.Result: These beans [oddly] are white.Case: These beans are from this bag.

Peirce 1883 in "A Theory of Probable Inference" (Studies in Logic) equated hypothetical inference with the induction of characters of objects (as he had done in effect before[119]). Eventually dissatisfied, by 1900 he distinguished them once and for all and also wrote that he now took the syllogistic forms and the doctrine of logical extension and comprehension as being less basic than he had thought. In 1903 he presented the following logical form for abductive inference:[136]

The surprising fact, C, is observed;

But if A were true, C would be a matter of course,

Hence, there is reason to suspect that A is true.

The logical form does not also cover induction, since induction neither depends on surprise nor proposes a new idea for its conclusion. Induction seeks facts to test a hypothesis; abduction seeks a hypothesis to account for facts. "Deduction proves that something must be; Induction shows that something actually is operative; Abduction merely suggests that something may be."[137] Peirce did not remain quite convinced that one logical form covers all abduction.[138] In his methodeutic or theory of inquiry (see below), he portrayed abduction as an economic initiative to further inference and study, and portrayed all three modes as clarified by their coordination in essential roles in inquiry: hypothetical explanation, deductive prediction, inductive testing.

Consider what effects that might conceivably have practical bearings you conceive the objects of your conception to have. Then, your conception of those effects is the whole of your conception of the object.

As a movement, pragmatism began in the early 1870s in discussions among Peirce, William James, and others in the Metaphysical Club. James among others regarded some articles by Peirce such as "The Fixation of Belief" (1877) and especially "How to Make Our Ideas Clear" (1878) as foundational to pragmatism.[139] Peirce (CP 5.11–12), like James (Pragmatism: A New Name for Some Old Ways of Thinking, 1907), saw pragmatism as embodying familiar attitudes, in philosophy and elsewhere, elaborated into a new deliberate method for fruitful thinking about problems. Peirce differed from James and the early John Dewey, in some of their tangential enthusiasms, in being decidedly more rationalistic and realistic, in several senses of those terms, throughout the preponderance of his own philosophical moods.

In 1905 Peirce coined the new name pragmaticism "for the precise purpose of expressing the original definition", saying that "all went happily" with James's and F.C.S. Schiller's variant uses of the old name "pragmatism" and that he coined the new name because of the old name's growing use in "literary journals, where it gets abused". Yet he cited as causes, in a 1906 manuscript, his differences with James and Schiller and, in a 1908 publication, his differences with James as well as literary author Giovanni Papini's declaration of pragmatism's indefinability. Peirce in any case regarded his views that truth is immutable and infinity is real, as being opposed by the other pragmatists, but he remained allied with them on other issues.[140]

Pragmatism begins with the idea that belief is that on which one is prepared to act. Peirce's pragmatism is a method of clarification of conceptions of objects. It equates any conception of an object to a conception of that object's effects to a general extent of the effects' conceivable implications for informed practice. It is a method of sorting out conceptual confusions occasioned, for example, by distinctions that make (sometimes needed) formal yet not practical differences. He formulated both pragmatism and statistical principles as aspects of scientific logic, in his "Illustrations of the Logic of Science" series of articles. In the second one, "How to Make Our Ideas Clear", Peirce discussed three grades of clearness of conception:

Clearness of a conception familiar and readily used, even if unanalyzed and undeveloped.

Clearness of a conception in virtue of clearness of its parts, in virtue of which logicians called an idea "distinct", that is, clarified by analysis of just what makes it applicable. Elsewhere, echoing Kant, Peirce called a likewise distinct definition "nominal" (CP 5.553).

Clearness in virtue of clearness of conceivable practical implications of the object's conceived effects, such as fosters fruitful reasoning, especially on difficult problems. Here he introduced that which he later called the pragmatic maxim.

By way of example of how to clarify conceptions, he addressed conceptions about truth and the real as questions of the presuppositions of reasoning in general. In clearness's second grade (the "nominal" grade), he defined truth as a sign's correspondence to its object, and the real as the object of such correspondence, such that truth and the real are independent of that which you or I or any actual, definite community of inquirers think. After that needful but confined step, next in clearness's third grade (the pragmatic, practice-oriented grade) he defined truth as that opinion which would be reached, sooner or later but still inevitably, by research taken far enough, such that the real does depend on that ideal final opinion—a dependence to which he appeals in theoretical arguments elsewhere, for instance for the long-run validity of the rule of induction.[141] Peirce argued that even to argue against the independence and discoverability of truth and the real is to presuppose that there is, about that very question under argument, a truth with just such independence and discoverability.

Peirce said that a conception's meaning consists in "all general modes of rational conduct" implied by "acceptance" of the conception—that is, if one were to accept, first of all, the conception as true, then what could one conceive to be consequent general modes of rational conduct by all who accept the conception as true?—the whole of such consequent general modes is the whole meaning. His pragmatism does not equate a conception's meaning, its intellectual purport, with the conceived benefit or cost of the conception itself, like a meme (or, say, propaganda), outside the perspective of its being true, nor, since a conception is general, is its meaning equated with any definite set of actual consequences or upshots corroborating or undermining the conception or its worth. His pragmatism also bears no resemblance to "vulgar" pragmatism, which misleadingly connotes a ruthless and Machiavellian search for mercenary or political advantage. Instead the pragmatic maxim is the heart of his pragmatism as a method of experimentational mental reflection[142] arriving at conceptions in terms of conceivable confirmatory and disconfirmatory circumstances—a method hospitable to the formation of explanatory hypotheses, and conducive to the use and improvement of verification.[143]

Peirce's pragmatism, as method and theory of definitions and conceptual clearness, is part of his theory of inquiry,[144] which he variously called speculative, general, formal or universal rhetoric or simply methodeutic.[117] He applied his pragmatism as a method throughout his work.

Critical common-sensism,[145] treated by Peirce as a consequence of his pragmatism, is his combination of Thomas Reid's common-sense philosophy with a fallibilism that recognizes that propositions of our more or less vague common sense now indubitable may later come into actual question, for example because of science's transformation of our world. It includes efforts to work up genuine doubts in tests for a core group of common indubitables that varies slowly if at all.

In The Fixation of Belief (1877), Peirce described inquiry in general not as the pursuit of truth per se but as the struggle to move from irritating, inhibitory doubt born of surprise, disagreement, and the like, and to reach a secure belief, belief being that on which one is prepared to act. That let Peirce frame scientific inquiry as part of a broader spectrum and as spurred, like inquiry generally, by actual doubt, not mere verbal, quarrelsome, or hyperbolic doubt, which he held to be fruitless. Peirce sketched four methods of settling opinion, ordered from least to most successful:

The method of tenacity (policy of sticking to initial belief) — which brings comforts and decisiveness but leads to trying to ignore contrary information and others' views as if truth were intrinsically private, not public. The method goes against the social impulse and easily falters since one may well notice when another's opinion seems as good as one's own initial opinion. Its successes can be brilliant but tend to be transitory.

The method of authority — which overcomes disagreements but sometimes brutally. Its successes can be majestic and long-lasting, but it cannot regulate people thoroughly enough to withstand doubts indefinitely, especially when people learn about other societies present and past.

The method of the a priori — which promotes conformity less brutally but fosters opinions as something like tastes, arising in conversation and comparisons of perspectives in terms of "what is agreeable to reason." Thereby it depends on fashion in paradigms and goes in circles over time. It is more intellectual and respectable but, like the first two methods, sustains accidental and capricious beliefs, destining some minds to doubt it.

The method of science — wherein inquiry supposes that the real is discoverable but independent of particular opinion, such that, unlike in the other methods, inquiry can, by its own account, go wrong (fallibilism), not only right, and thus purposely tests itself and criticizes, corrects, and improves itself.

Peirce held that, in practical affairs, slow and stumbling ratiocination is often dangerously inferior to instinct and traditional sentiment, and that the scientific method is best suited to theoretical research,[146] which in turn should not be trammeled by the other methods and practical ends; reason's "first rule"[112] is that, in order to learn, one must desire to learn and, as a corollary, must not block the way of inquiry. Scientific method excels the others finally by being deliberately designed to arrive — eventually — at the most secure beliefs, upon which the most successful practices can be based. Starting from the idea that people seek not truth per se but instead to subdue irritating, inhibitory doubt, Peirce showed how, through the struggle, some can come to submit to truth for the sake of belief's integrity, seek as truth the guidance of potential conduct correctly to its given goal, and wed themselves to the scientific method.

Active, abductive genesis of theory, with no prior assurance of truth;

Deductive application of the contingent theory so as to clarify its practical implications;

Inductive testing and evaluation of the provisional theory's utility for the anticipation of future experience, in both senses: prediction and control.

Thereby he fleshed out an approach to inquiry far more solid than the flatter image of inductive generalization simpliciter, which is a mere relabeling of phenomenological patterns. Peirce's pragmatism was the first time the scientific method was proposed as an epistemology for philosophical questions.

A theory that succeeds better than its rivals in predicting and controlling our world is said to be nearer the truth. This is an operational notion of truth used by scientists.

Peirce extracted the pragmatic model or theory of inquiry from its raw materials in classical logic and refined it in parallel with the early development of symbolic logic to address problems about the nature of scientific reasoning.

Abduction, deduction, and induction make incomplete sense in isolation from one another but comprise a cycle understandable as a whole insofar as they collaborate toward inquiry's end. In the pragmatic way of thinking in terms of conceivable practical implications, every thing has a purpose, and its purpose is the first thing that we should try to note about it. Abduction hypothesizes an explanation for deduction to clarify into implications to be tested so that induction can evaluate the hypothesis, in the struggle to move from troublesome uncertainty to secure belief. No matter how traditional and needful it is to study the modes of inference in abstraction from one another, inquiry's integrity strongly limits the effective modularity of inquiry's principal components.

Peirce's outline of the scientific method in §III–IV of "A Neglected Argument"[147] is summarized below (except as otherwise noted). There he also reviewed plausibility and inductive precision (issues of critique of arguments).

1. Abductive (or retroductive) phase. Guessing, inference to explanatory hypotheses for selection of those best worth trying. From abduction, Peirce distinguishes induction as inferring, on the basis of tests, the proportion of truth in the hypothesis. Every inquiry, whether into ideas, brute facts, or norms and laws, arises from surprising observations in one or more of those realms (and for example at any stage of an inquiry already underway). All explanatory content of theories comes from abduction, which guesses a new or outside idea so as to account in a simple, economical way for a surprising or complicated phenomenon. Oftenest even a well-prepared mind guesses wrong. But the modicum of success of our guesses far exceeds that of random luck, and seems born of attunement to nature by instincts developed or inherent, especially insofar as best guesses are optimally plausible and simple in the sense of the "facile and natural", as by Galileo's natural light of reason and as distinct from "logical simplicity".[148] Abduction is the most fertile but least secure mode of inference. Its general rationale is inductive: it succeeds often enough and it has no substitute in expediting us toward new truths.[149] In 1903 Peirce called pragmatism "the logic of abduction".[150] It points to efficiency. Coordinative method leads from abducing a plausible hypothesis to judging it for its testability[151] and for how its trial would economize inquiry itself.[152] The hypothesis, being insecure, needs to have practical implications leading at least to mental tests and, in science, lending themselves to scientific tests. A simple but unlikely guess, if uncostly to test for falsity, may belong first in line for testing. A guess is intrinsically worth testing if it has instinctive plausibility or reasoned objective probability, while subjective likelihood, though reasoned, can be misleadingly seductive. Guesses can be chosen for trial strategically, for their caution (for which Peirce gave as example the game of Twenty Questions), breadth, or incomplexity.[153] One can hope to discover only that which time would reveal through a learner's sufficient experience anyway, so the point is to expedite it; economy of research is what demands the leap, so to speak, of abduction and governs its art.[152]

2. Deductive phase. Two stages:

i. Explication. Unclearly premissed, but deductive, analysis of the hypothesis so as to render its parts as clear as possible.

3. Inductive phase. Evaluation of the hypothesis, inferring from observational or experimental tests of its deduced consequences. The long-run validity of the rule of induction is deducible from the principle (presuppositional to reasoning in general) that the real "is only the object of the final opinion to which sufficient investigation would lead";[141] anything to which no such process would ever lead would not be real. Induction involving the ongoing accumulation of evidence follows "a method which, sufficiently persisted in," will "diminish the error below any predesignate degree." Three stages:

i. Classification. Unclearly premissed, but inductive, classing of objects of experience under general ideas.

ii. Probation: direct Inductive Argumentation. Crude or Gradual. Crude Induction, founded on experience in one mass (CP 2.759), presumes that future experience on a question will not differ utterly from all past experience (CP 2.756). Gradual Induction makes a new estimate of the proportion of truth in the hypothesis after each test, and is Qualitative or Quantitative. Qualitative Induction depends on estimating the relative evidential weights of the various qualities of the subject class under investigation (CP 2.759; see also CP 7.114–20). Quantitative Induction depends on how often, in a fair sample of instances of S, S is found actually accompanied by P that was predicted for S (CP 2.758). It depends on measurements, or statistics, or counting.

iii. Sentential Induction. "...which, by Inductive reasonings, appraises the different Probations singly, then their combinations, then makes self-appraisal of these very appraisals themselves, and passes final judgment on the whole result".

Peirce drew on the methodological implications of the four incapacities — no genuine introspection, no intuition in the sense of non-inferential cognition, no thought but in signs, and no conception of the absolutely incognizable — to attack philosophical Cartesianism, of which he said that:[119]

1. "It teaches that philosophy must begin in universal doubt" — when, instead, we start with preconceptions, "prejudices [...] which it does not occur to us can be questioned", though we may find reason to question them later. "Let us not pretend to doubt in philosophy what we do not doubt in our hearts."

2. "It teaches that the ultimate test of certainty is...in the individual consciousness" — when, instead, in science a theory stays on probation till agreement is reached, then it has no actual doubters left. No lone individual can reasonably hope to fulfill philosophy's multi-generational dream. When "candid and disciplined minds" continue to disagree on a theoretical issue, even the theory's author should feel doubts about it.

3. It trusts to "a single thread of inference depending often upon inconspicuous premisses" — when, instead, philosophy should, "like the successful sciences", proceed only from tangible, scrutinizable premisses and trust not to any one argument but instead to "the multitude and variety of its arguments" as forming, not a chain at least as weak as its weakest link, but "a cable whose fibers", soever "slender, are sufficiently numerous and intimately connected".

4. It renders many facts "absolutely inexplicable, unless to say that 'God makes them so' is to be regarded as an explanation"[154] — when, instead, philosophy should avoid being "unidealistic",[155] misbelieving that something real can defy or evade all possible ideas, and supposing, inevitably, "some absolutely inexplicable, unanalyzable ultimate", which explanatory surmise explains nothing and so is inadmissible.

Ontology. Peirce was a Scholastic Realist, declaring for the reality of generals as early as 1868.[156] Regarding modalities (possibility, necessity, etc.), he came in later years to regard himself as having wavered earlier as to just how positively real the modalities are. In his 1897 "The Logic of Relatives" he wrote:

I formerly defined the possible as that which in a given state of information (real or feigned) we do not know not to be true. But this definition today seems to me only a twisted phrase which, by means of two negatives, conceals an anacoluthon. We know in advance of experience that certain things are not true, because we see they are impossible.

Peirce retained, as useful for some purposes, the definitions in terms of information states, but insisted that the pragmaticist is committed to a strong modal realism by conceiving of objects in terms of predictive general conditional propositions about how they would behave under certain circumstances.[157]

Psychical or Religious Metaphysics. Peirce believed in God, and characterized such belief as founded in an instinct explorable in musing over the worlds of ideas, brute facts, and evolving habits — and it is a belief in God not as an actual or existent being (in Peirce's sense of those words), but all the same as a real being.[158] In "A Neglected Argument for the Reality of God" (1908),[147] Peirce sketches, for God's reality, an argument to a hypothesis of God as the Necessary Being, a hypothesis which he describes in terms of how it would tend to develop and become compelling in musement and inquiry by a normal person who is led, by the hypothesis, to consider as being purposed the features of the worlds of ideas, brute facts, and evolving habits (for example scientific progress), such that the thought of such purposefulness will "stand or fall with the hypothesis"; meanwhile, according to Peirce, the hypothesis, in supposing an "infinitely incomprehensible" being, starts off at odds with its own nature as a purportively true conception, and so, no matter how much the hypothesis grows, it both (A) inevitably regards itself as partly true, partly vague, and as continuing to define itself without limit, and (B) inevitably has God appearing likewise vague but growing, though God as the Necessary Being is not vague or growing; but the hypothesis will hold it to be more false to say the opposite, that God is purposeless. Peirce also argued that the will is free[159] and (see Synechism) that there is at least an attenuated kind of immortality.

Physical Metaphysics. Peirce held the view, which he called objective idealism, that "matter is effete mind, inveterate habits becoming physical laws".[160] Peirce asserted the reality of (1) absolute chance (his tychist view), (2) mechanical necessity (anancist view), and (3) that which he called the law of love (agapist view), echoing his categories Firstness, Secondness, and Thirdness, respectively. He held that fortuitous variation (which he also called "sporting"), mechanical necessity, and creative love are the three modes of evolution (modes called "tychasm", "anancasm", and "agapasm")[161] of the cosmos and its parts. He found his conception of agapasm embodied in Lamarckian evolution; the overall idea in any case is that of evolution tending toward an end or goal, and it could also be the evolution of a mind or a society; it is the kind of evolution which manifests workings of mind in some general sense. He said that overall he was a synechist, holding with reality of continuity,[162] especially of space, time, and law.[163]

Peirce outlined two fields, "Cenoscopy" and "Science of Review", both of which he called philosophy. Both included philosophy about science. In 1903 he arranged them, from more to less theoretically basic, thus:[100]

Science of Discovery.

Mathematics.

Cenoscopy (philosophy as discussed earlier in this article—categorial, normative, metaphysical), as First Philosophy, concerns positive phenomena in general, does not rely on findings from special sciences, and includes the general study of inquiry and scientific method.

Idioscopy, or the Special Sciences (of nature and mind).

Science of Review, as Ultimate Philosophy, arranges "...the results of discovery, beginning with digests, and going on to endeavor to form a philosophy of science". His examples included Humboldt's Cosmos, Comte's Philosophie positive, and Spencer's Synthetic Philosophy.

Practical Science, or the Arts.

Peirce placed, within Science of Review, the work and theory of classifying the sciences (including mathematics and philosophy). His classifications, on which he worked for many years, draw on argument and wide knowledge, and are of interest both as a map for navigating his philosophy and as an accomplished polymath's survey of research in his time.

^Joseph Brent (1998). Charles Sanders Peirce: A Life (2 ed.). Indiana University Press. p. 18. ISBN9780253211613. Peirce had strong, though unorthodox, religious convictions. Although he was a communicant in the Episcopal church for most of his life, he expressed contempt for the theologies, metaphysics, and practices of established religions.|accessdate= requires |url= (help)

^"Peirce", in the case of C.S. Peirce, always rhymes with the English-language word "terse" and so, in most dialects, is pronounced exactly like the English-language word "purse(help·info)". See "Note on the Pronunciation of 'Peirce'", Peirce Project Newsletter, v. 1, nos. 3/4, Dec. 1994.

^Weiss, Paul (1934), "Peirce, Charles Sanders" in the Dictionary of American Biography. ArisbeEprint.

^ abAnellis, Irving H. (1995), "Peirce Rustled, Russell Pierced: How Charles Peirce and Bertrand Russell Viewed Each Other's Work in Logic, and an Assessment of Russell's Accuracy and Role in the Historiography of Logic", Modern Logic 5, 270–328. ArisbeEprint.

^"The manuscript material now (1997) comes to more than a hundred thousand pages. These contain many pages of no philosophical interest, but the number of pages on philosophy certainly number much more than half of that. Also, a significant but unknown number of manuscripts have been lost." — Joseph Ransdell (1997), "Some Leading Ideas of Peirce's Semiotic", end note 2, 1997 light revision of 1977 version in Semiotica 19:157–78.

^ abPeirce (1885), "On the Algebra of Logic: A Contribution to the Philosophy of Notation", American Journal of Mathematics 7, two parts, first part published 1885, pp. 180–202 (see Houser in linked paragraph in "Introduction" in W 4). Presented, National Academy of Sciences, Newport, RI, 14–17 October 1884 (see EP 1, Headnote 16). 1885 is the year usually given for this work. Reprinted CP 3.359–403, W 5:162–90, EP 1:225–8, in part.

^Peirce (1903 MS), CP 6.176: "But I now define a pseudo-continuum as that which modern writers on the theory of functions call a continuum. But this is fully represented by [...] the totality of real values, rational and irrational [...]."

^ abThe ground blackness is the pure abstraction of the quality black. Something black is something embodying blackness, pointing us back to the abstraction. The quality black amounts to reference to its own pure abstraction, the ground blackness. The question is not merely of noun (the ground) versus adjective (the quality), but rather of whether we are considering the black(ness) as abstracted away from application to an object, or instead as so applied (for instance to a stove). Yet note that Peirce's distinction here is not that between a property-general and a property-individual (a trope). See "On a New List of Categories" (1867), in the section appearing in CP 1.551. Regarding the ground, cf. the Scholastic conception of a relation's foundation, Google limited preview Deely 1982, p. 61

^A quale in this sense is a such, just as a quality is a suchness. Cf. under "Use of Letters" in §3 of Peirce's "Description of a Notation for the Logic of Relatives", Memoirs of the American Academy, v. 9, pp. 317–78 (1870), separately reprinted (1870), from which see p. 6 via Google books, also reprinted in CP 3.63:

Now logical terms are of three grand classes. The first embraces those whose logical form involves only the conception of quality, and which therefore represent a thing simply as “a —.” These discriminate objects in the most rudimentary way, which does not involve any consciousness of discrimination. They regard an object as it is in itself as such (quale); for example, as horse, tree, or man. These are absolute terms. (Peirce, 1870. But also see "Quale-Consciousness", 1898, in CP 6.222–37.)

...death makes the number of our risks, the number of our inferences, finite, and so makes their mean result uncertain. The very idea of probability and of reasoning rests on the assumption that this number is indefinitely great. .... ...logicality inexorably requires that our interests shall not be limited. .... Logic is rooted in the social principle.

^ abSee pp. 404–9 in "Pragmatism" in EP 2. Ten quotes on collateral experience from Peirce provided by Joseph Ransdell can be viewed here at peirce-l's Lyris archive. Note: Ransdell's quotes from CP 8.178–9 are also in EP 2:493–4, which gives their date as 1909; and his quote from CP 8.183 is also in EP 2:495–6, which gives its date as 1909.

I define a Sign as anything which is so determined by something else, called its Object, and so determines an effect upon a person, which effect I call its Interpretant, that the latter is thereby mediately determined by the former. My insertion of "upon a person" is a sop to Cerberus, because I despair of making my own broader conception understood.

^"Representamen", properly with the 'a' long and stressed (/rɛprəzɛnˈteɪmən/rep-rə-zen-TAY-mən), was adopted (not coined) by Peirce as his technical term for the sign as covered in his theory, in case a divergence should come to light between his theoretical version and the popular senses of the word "sign". He eventually stopped using "representamen". See EP 2:272–3 and Semiotic and Significs p. 193, quotes in "Representamen" at CDPT.

^ abPeirce (1903 MS), "Nomenclature and Divisions of Triadic Relations, as Far as They Are Determined", under other titles in Collected Papers (CP) v. 2, paragraphs 233–72, and reprinted under the original title in Essential Peirce (EP) v. 2, pp. 289–99. Also see image of MS 339 (August 7, 1904) supplied to peirce-l by Bernard Morand of the Institut Universitaire de Technologie (France), Département Informatique.

^ ab"That the rule of induction will hold good in the long run may be deduced from the principle that reality is only the object of the final opinion to which sufficient investigation would lead", in Peirce (1878 April), "The Probability of Induction", p. 718 (via Internet Archive ) in Popular Science Monthly, v. 12, pp. 705–18. Reprinted in CP 2.669–93, W 3:290–305, EP 1:155–69, elsewhere.

Consequently, to discover is simply to expedite an event that would occur sooner or later, if we had not troubled ourselves to make the discovery. Consequently, the art of discovery is purely a question of economics. The economics of research is, so far as logic is concerned, the leading doctrine with reference to the art of discovery. Consequently, the conduct of abduction, which is chiefly a question of heuretic and is the first question of heuretic, is to be governed by economical considerations.

^Peirce, C. S., "On the Logic of Drawing Ancient History from Documents", EP 2, see 107-9. On Twenty Questions, see 109:

Lane, Robert (2007), "Peirce's Modal Shift: From Set Theory to Pragmaticism", Journal of the History of Philosophy, v. 45, n. 4.

^Peirce in his 1906 "Answers to Questions concerning my Belief in God", CP 6.495, Eprint, reprinted in part as "The Concept of God" in Philosophical Writings of Peirce, J. Buchler, ed., 1940, pp. 375–8:

I will also take the liberty of substituting "reality" for "existence." This is perhaps overscrupulosity; but I myself always use exist in its strict philosophical sense of "react with the other like things in the environment." Of course, in that sense, it would be fetichism to say that God "exists." The word "reality," on the contrary, is used in ordinary parlance in its correct philosophical sense. [....] I define the real as that which holds its characters on such a tenure that it makes not the slightest difference what any man or men may have thought them to be, or ever will have thought them to be, here using thought to include, imagining, opining, and willing (as long as forcible means are not used); but the real thing's characters will remain absolutely untouched.